List Casting Overview

1 Introduction

Hierarchical data is surprisingly common, and are commonly represented in by nested lists.

Broadcasted operations can be performed over dimensions, but not through nesting or hierarchies.
Therefore, it is useful to be able to cast nested lists into dimensional lists.
The ‘broadcast’ package provides the cast_hier2dim() function, to cast nested lists into dimensional lists, and the cast_dim2hier() to cast dimensional lists back to nested lists.

Casting between nested and dimensional lists is not only useful for broadcasting, however.
Casting nested lists to dimensional lists has its own merits, as dimensional lists have some advantages over nested lists beside the broadcasting, such as the following:

• Performing sub-set operations on multiple recursive subsets (using the [[ and [[<- operators) requires a (potentially slow) loop, whereas multi-dimensional subsets (using operator forms like [..., ...] and [..., ...]<-) are vectorized and generally much faster.
• Re-organizing dimensions of a recursive array is generally much easier, faster, and more straight-forward than re-organizing hierarchies of a nested list.

This Vignette gives an overview of the functions ‘broadcast’ provides to cast between nested and dimensional lists.

 

2 Cast Hierarchical List to Dimensional List

2.1 Introduction

The cast_hier2dim() function casts a nested list into a dimensional list.
This section gently introduces the properties of this function through a series of examples, where each subsequent example builds on the previous one.
Familiarity with nested lists and dimensional lists (i.e. arrays of type list) is essential to follow these examples.

 

2.2 Example 1: Basics

For a first example, consider the following list:

x <- list(
  group1 = list(
    class1 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    ),
    class2 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    )
  ),
  group2 = list(
    class1 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    ),
    class2 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    )
  )
)

Before actually casting x into a dimensional list, one may want to know what the dimensions will become when casted as a dimensional list;
The hier2dim() function shows you that:

hier2dim(x)
#>       
#> 3 2 2

It returns the dimensions c(3, 2, 2).

Let’s now cast x as a dimensional list:

x2 <- cast_hier2dim(x) # actually cast nested list into dimensional list
print(x2)
#> , , 1
#> 
#>      [,1]         [,2]        
#> [1,] numeric,10   numeric,10  
#> [2,] numeric,10   numeric,10  
#> [3,] character,10 character,10
#> 
#> , , 2
#> 
#>      [,1]         [,2]        
#> [1,] numeric,10   numeric,10  
#> [2,] numeric,10   numeric,10  
#> [3,] character,10 character,10

Using the default arguments, element x[[i]][[j]][[k]] corresponds to element x2[k, j, i] (for all i, j, and k).
This can be changed, as will be shown in a later example.

As shown in the results above, cast_hier2dim() will obviously not preserve names.
It is trivially easy to set the dimnames of x2, using hiernames2dimnames() (available from version 0.1.5):

dimnames(x2) <- hiernames2dimnames(x)
print(x2)
#> , , group1
#> 
#>        class1       class2      
#> height numeric,10   numeric,10  
#> weight numeric,10   numeric,10  
#> sex    character,10 character,10
#> 
#> , , group2
#> 
#>        class1       class2      
#> height numeric,10   numeric,10  
#> weight numeric,10   numeric,10  
#> sex    character,10 character,10

There, the names are now correct.

As shown above, will display a dimensional list more compactly than a nested list.
Depending on the situation this may be either be desirable or undesirable.

One can print x2 less compactly without much effort by flattening it, using the cast_dim2flat() function.
We only need to see a portion of the list in detail, so let’s look at class1 from group 1 in the flattened form:

cast_dim2flat(x2[, 1, "group1", drop = FALSE])
#> $`['height', 'class1', 'group1']`
#>  [1] 170.5506 171.0474 170.5501 170.4225 170.5586 168.1398 169.5181 170.4771
#>  [9] 170.8119 170.6366
#> 
#> $`['weight', 'class1', 'group1']`
#>  [1] 80.12057 80.78809 81.07633 79.46860 77.59170 80.88402 76.71234 78.81424
#>  [9] 80.54552 82.02587
#> 
#> $`['sex', 'class1', 'group1']`
#>  [1] "M" "M" "M" "M" "M" NA  NA  NA  "M" "F"

 

Dimensional lists can be easier to work with than hierarchical lists.
Consider, for example, printing the height of the first class of every group in a list - let’s compare how to do this in a nested list vs a dimensional list.

With a nested list, doing this takes a slow, messy for-loop:

for(i in seq_along(x)) {
  print(names(x)[i])
  x[[i]][[1]][["height"]] |> print() # slow for-loop, messy code
}
#> [1] "group1"
#>  [1] 170.5506 171.0474 170.5501 170.4225 170.5586 168.1398 169.5181 170.4771
#>  [9] 170.8119 170.6366
#> [1] "group2"
#>  [1] 169.7132 168.8474 170.3181 169.9918 171.5054 172.2852 169.9928 168.9357
#>  [9] 169.0923 168.4938

With a dimensional list, the very same thing can be done with sleek, vectorized code; no messy loop needed:

x2["height", 1L, ] |> print()
#> $group1
#>  [1] 170.5506 171.0474 170.5501 170.4225 170.5586 168.1398 169.5181 170.4771
#>  [9] 170.8119 170.6366
#> 
#> $group2
#>  [1] 169.7132 168.8474 170.3181 169.9918 171.5054 172.2852 169.9928 168.9357
#>  [9] 169.0923 168.4938

x2["height", 1L, , drop = FALSE] |> cast_dim2flat() # same but more informative
#> $`['height', 'class1', 'group1']`
#>  [1] 170.5506 171.0474 170.5501 170.4225 170.5586 168.1398 169.5181 170.4771
#>  [9] 170.8119 170.6366
#> 
#> $`['height', 'class1', 'group2']`
#>  [1] 169.7132 168.8474 170.3181 169.9918 171.5054 172.2852 169.9928 168.9357
#>  [9] 169.0923 168.4938

It is also easier to re-arrange dimensions - for example using aperm() - than it is to re-arrange hierarchies.

 

2.3 Example 2: Cast from outside to inside

In Example 1, the default arguments were used for cast_hier2dim().
One of these arguments is in2out, which defaults to TRUE.

Consider a nested list x with a depth of 3, and a dimensional list X2 with 3 dimensions, where the relationship between x and x2 can be expressed as x2 <- cast_hier2dim(x, ...).
Given this, the following can be stated about in2out:

• If in2out = TRUE, which is the default and used in Example 1, element x[[i]][[j]][[k]] corresponds to element x2[k, j, i] (for all i, j, and k).
  
• If in2out = FALSE, element x[[i]][[j]][[k]] corresponds to element x2[i, j, k] (for all i, j, and k).

The default of in2out = TRUE was chosen, because elements in subsequent rows are close to each other, while elements in subsequent layers (third dimension) are generally not close to each other, and the default of in2out = TRUE attempts to retain that behaviour.

For this example, the same list will be used as in Example 1:

x <- list(
  group1 = list(
    class1 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    ),
    class2 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    )
  ),
  group2 = list(
    class1 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    ),
    class2 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    )
  )
)

Let’s once again cast this list to a dimensional list, but this time use in2out = FALSE:

hier2dim(x, in2out = FALSE) # check once again the dimensions
#>       
#> 2 2 3
x2 <- cast_hier2dim(x, in2out = FALSE) # actually cast nested list into dimensional list
print(x2)
#> , , 1
#> 
#>      [,1]       [,2]      
#> [1,] numeric,10 numeric,10
#> [2,] numeric,10 numeric,10
#> 
#> , , 2
#> 
#>      [,1]       [,2]      
#> [1,] numeric,10 numeric,10
#> [2,] numeric,10 numeric,10
#> 
#> , , 3
#> 
#>      [,1]         [,2]        
#> [1,] character,10 character,10
#> [2,] character,10 character,10

x2 is the casted list. Since in2out = FALSE, element x[[i]][[j]][[k]] corresponds to element x2[i, j, k] (for all i, j, and k).

Once again it is trivially easy to set the dimnames of x2, using hiernames2dimnames() (available from version 0.1.5):

# this time, in2out = FALSE
# so we go from the surface names to the deepest names
dimnames(x2) <- hiernames2dimnames(x, in2out = FALSE)
print(x2)
#> , , height
#> 
#>        class1     class2    
#> group1 numeric,10 numeric,10
#> group2 numeric,10 numeric,10
#> 
#> , , weight
#> 
#>        class1     class2    
#> group1 numeric,10 numeric,10
#> group2 numeric,10 numeric,10
#> 
#> , , sex
#> 
#>        class1       class2      
#> group1 character,10 character,10
#> group2 character,10 character,10

There, the names are now correct.

One can print x2 less compactly without much effort by flattening it, again using the cast_dim2flat() function.
We only need to see a portion of the list in detail, so let’s look at class1 from group 1 in the flattened form:

cast_dim2flat(x2["group1", 1, , drop = FALSE])
#> $`['group1', 'class1', 'height']`
#>  [1] 171.0771 170.6319 173.0345 169.1913 168.9309 170.3470 170.1769 170.1982
#>  [9] 168.3893 170.1433
#> 
#> $`['group1', 'class1', 'weight']`
#>  [1] 80.16081 81.50925 81.71725 79.22869 77.59525 79.32399 79.28889 79.94429
#>  [9] 78.95529 77.89471
#> 
#> $`['group1', 'class1', 'sex']`
#>  [1] NA  NA  NA  "M" NA  "F" "M" "M" "M" "M"

 

2.4 Example 3: Padding

For Example 3, we take the same list as before, but remove x$group1$class2:

x <- list(
  group1 = list(
    class1 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    )
  ),
  group2 = list(
    class1 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    ),
    class2 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    )
  )
)

Let’s first check what dimensions it will get when casted using hier2dim():

hier2dim(x)
#>         padding         
#>       3       2       2

The dimensions are the same as in Example 1: c(3, 2, 2).
But notice the names of the output are different: the second element has the name “padding”; this indicates that some columns won’t have enough elements to completely fill the column, and so additional elements will be added as padding.

So let’s cast this list as dimensional:

x2 <- cast_hier2dim(x)
print(x2)
#> , , 1
#> 
#>      [,1]         [,2]
#> [1,] numeric,10   NULL
#> [2,] numeric,10   NULL
#> [3,] character,10 NULL
#> 
#> , , 2
#> 
#>      [,1]         [,2]        
#> [1,] numeric,10   numeric,10  
#> [2,] numeric,10   numeric,10  
#> [3,] character,10 character,10

Subset x2[, 2, 1] is filled with NULL; this is the place where x$group1$class2 was in Example 1, but since it’s not there, we need to fill something.

To make it make obvious, let’s give the array proper dimnames:

dimnames(x2) <- hiernames2dimnames(x)
print(x2)
#> , , group1
#> 
#>        class1       class2
#> height numeric,10   NULL  
#> weight numeric,10   NULL  
#> sex    character,10 NULL  
#> 
#> , , group2
#> 
#>        class1       class2      
#> height numeric,10   numeric,10  
#> weight numeric,10   numeric,10  
#> sex    character,10 character,10

Again, element “class2” is missing from element “group1”, but not from “group2”, and so padded with NULL when the list is casted as dimensional.

Sometimes, a different value than NULL is desired for padding.
So let’s replace the padding value with something really obvious, using the padding argument:

x2 <- cast_hier2dim(x, padding = list(~ "this is padding!"))
dimnames(x2) <- hiernames2dimnames(x)
print(x2)
#> , , group1
#> 
#>        class1       class2             
#> height numeric,10   ~"this is padding!"
#> weight numeric,10   ~"this is padding!"
#> sex    character,10 ~"this is padding!"
#> 
#> , , group2
#> 
#>        class1       class2      
#> height numeric,10   numeric,10  
#> weight numeric,10   numeric,10  
#> sex    character,10 character,10

Once again, one can print or present x2 less compactly by flattening it:

cast_dim2flat(x2)
#> $`['height', 'class1', 'group1']`
#>  [1] 170.1371 169.6202 170.2695 170.0284 170.6253 169.8556 169.9827 171.0455
#>  [9] 168.8739 169.9475
#> 
#> $`['weight', 'class1', 'group1']`
#>  [1] 81.83807 80.19819 79.11968 80.89755 81.49745 79.43180 80.51198 79.46472
#>  [9] 78.19809 78.76697
#> 
#> $`['sex', 'class1', 'group1']`
#>  [1] "M" "M" "M" NA  "F" "M" NA  "M" "M" "M"
#> 
#> $`['height', 'class2', 'group1']`
#> ~"this is padding!"
#> 
#> $`['weight', 'class2', 'group1']`
#> ~"this is padding!"
#> 
#> $`['sex', 'class2', 'group1']`
#> ~"this is padding!"
#> 
#> $`['height', 'class1', 'group2']`
#>  [1] 168.9559 171.1897 168.9700 169.6058 169.0339 170.8541 170.3411 169.0895
#>  [9] 172.0468 168.9393
#> 
#> $`['weight', 'class1', 'group2']`
#>  [1] 80.01244 81.13396 78.78732 79.59470 80.19193 81.35782 80.10036 81.26646
#>  [9] 80.02173 79.79764
#> 
#> $`['sex', 'class1', 'group2']`
#>  [1] "F" NA  "F" "M" "M" "F" "M" NA  "M" "F"
#> 
#> $`['height', 'class2', 'group2']`
#>  [1] 171.8068 171.9164 170.6215 168.5649 168.6526 170.0644 169.3544 169.7386
#>  [9] 170.5551 170.8431
#> 
#> $`['weight', 'class2', 'group2']`
#>  [1] 80.98423 80.67686 81.21165 81.49650 79.72600 82.28893 78.59625 79.33094
#>  [9] 78.46250 80.84236
#> 
#> $`['sex', 'class2', 'group2']`
#>  [1] "M" NA  NA  "M" "M" NA  "M" NA  "M" NA

 

2.5 Example 4: Comparing in2out with padding

In this example, the same nested list as from the previous example is used, to demonstrate the difference between in2out = TRUE (which is the default), and in2out = FALSE.

Consider first the original list again:

x <- list(
  group1 = list(
    class1 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    )
  ),
  group2 = list(
    class1 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    ),
    class2 = list(
      height = rnorm(10, 170),
      weight = rnorm(10, 80),
      sex = sample(c("M", "F", NA), 10, TRUE)
    )
  )
)

On the left side the list is casted as dimensional using the default of in2out = TRUE, with proper names assigned.
On the right side the list is casted as dimensional using in2out = FALSE, again with proper names assigned.

x2 <- cast_hier2dim(x)
dimnames(x2) <- hiernames2dimnames(x)
print(x2)
#> , , group1
#> 
#>        class1       class2
#> height numeric,10   NULL  
#> weight numeric,10   NULL  
#> sex    character,10 NULL  
#> 
#> , , group2
#> 
#>        class1       class2      
#> height numeric,10   numeric,10  
#> weight numeric,10   numeric,10  
#> sex    character,10 character,10

x2 <- cast_hier2dim(x, in2out = FALSE)
dimnames(x2) <- hiernames2dimnames(x, in2out = FALSE)
print(x2)
#> , , height
#> 
#>        class1     class2    
#> group1 numeric,10 NULL      
#> group2 numeric,10 numeric,10
#> 
#> , , weight
#> 
#>        class1     class2    
#> group1 numeric,10 NULL      
#> group2 numeric,10 numeric,10
#> 
#> , , sex
#> 
#>        class1       class2      
#> group1 character,10 NULL        
#> group2 character,10 character,10

 

3 Cast Dimensional List to Hierarchical list

‘broadcast’ provides the cast_dim2hier():
cast_dim2hier() takes a dimensional list (i.e. an array of type list), and casts it to a nested list.

Consider the following recursive array as an example:

x <- array(c(as.list(1:11), ~hello, as.list(month.abb)), c(4:2))
dimnames(x) <- list(
  letters[1:4],
  LETTERS[1:3],
  c("group1", "group2")
)
print(x)
#> , , group1
#> 
#>   A B C     
#> a 1 5 9     
#> b 2 6 10    
#> c 3 7 11    
#> d 4 8 ~hello
#> 
#> , , group2
#> 
#>   A     B     C    
#> a "Jan" "May" "Sep"
#> b "Feb" "Jun" "Oct"
#> c "Mar" "Jul" "Nov"
#> d "Apr" "Aug" "Dec"

Like cast_hier2dim(), cast_dim2hier() also has the in2out argument, which (again) defaults to TRUE.
Let’s cast the above dimensional list to a nested list, and compare the results when using in2out = TRUE (on the left) versus in2out = FALSE (on the right):

x2 <- cast_dim2hier(
  x, distr.names = TRUE
)
lobstr::tree(x2)
#> <list>
#> ├─group1: <list>
#> │ ├─A: <list>
#> │ │ ├─a: 1
#> │ │ ├─b: 2
#> │ │ ├─c: 3
#> │ │ └─d: 4
#> │ ├─B: <list>
#> │ │ ├─a: 5
#> │ │ ├─b: 6
#> │ │ ├─c: 7
#> │ │ └─d: 8
#> │ └─C: <list>
#> │   ├─a: 9
#> │   ├─b: 10
#> │   ├─c: 11
#> │   └─d: S3<formula> ~hello
#> └─group2: <list>
#>   ├─A: <list>
#>   │ ├─a: "Jan"
#>   │ ├─b: "Feb"
#>   │ ├─c: "Mar"
#>   │ └─d: "Apr"
#>   ├─B: <list>
#>   │ ├─a: "May"
#>   │ ├─b: "Jun"
#>   │ ├─c: "Jul"
#>   │ └─d: "Aug"
#>   └─C: <list>
#>     ├─a: "Sep"
#>     ├─b: "Oct"
#>     ├─c: "Nov"
#>     └─d: "Dec"

x2 <- cast_dim2hier(
  x, in2out = FALSE, distr.names = TRUE
)
lobstr::tree(x2)
#> <list>
#> ├─a: <list>
#> │ ├─A: <list>
#> │ │ ├─group1: 1
#> │ │ └─group2: "Jan"
#> │ ├─B: <list>
#> │ │ ├─group1: 5
#> │ │ └─group2: "May"
#> │ └─C: <list>
#> │   ├─group1: 9
#> │   └─group2: "Sep"
#> ├─b: <list>
#> │ ├─A: <list>
#> │ │ ├─group1: 2
#> │ │ └─group2: "Feb"
#> │ ├─B: <list>
#> │ │ ├─group1: 6
#> │ │ └─group2: "Jun"
#> │ └─C: <list>
#> │   ├─group1: 10
#> │   └─group2: "Oct"
#> ├─c: <list>
#> │ ├─A: <list>
#> │ │ ├─group1: 3
#> │ │ └─group2: "Mar"
#> │ ├─B: <list>
#> │ │ ├─group1: 7
#> │ │ └─group2: "Jul"
#> │ └─C: <list>
#> │   ├─group1: 11
#> │   └─group2: "Nov"
#> └─d: <list>
#>   ├─A: <list>
#>   │ ├─group1: 4
#>   │ └─group2: "Apr"
#>   ├─B: <list>
#>   │ ├─group1: 8
#>   │ └─group2: "Aug"
#>   └─C: <list>
#>     ├─group1: S3<formula> ~hello
#>     └─group2: "Dec"

The added distr.names = TRUE argument will distribute the dimnames in a logical way over the nested elements.

 

4 Data Wrangling Example: Turning list inside out

The cast functions can be used to turn a list inside out.

Let’s start with the following list:

x <- list(
  group1 = list(
    class1 = list(
      height = rnorm(5, 170) |> as.integer(),
      weight = rnorm(5, 80)  |> as.integer(),
      sex = sample(c("M", "F", NA), 5, TRUE)
    ),
    class2 = list(
      height = rnorm(5, 170)  |> as.integer(),
      weight = rnorm(5, 80) |> as.integer(),
      sex = sample(c("M", "F", NA), 5, TRUE)
    )
  ),
  group2 = list(
    class1 = list(
      height = rnorm(5, 170) |> as.integer(),
      weight = rnorm(5, 80) |> as.integer(),
      sex = sample(c("M", "F", NA), 5, TRUE)
    ),
    class2 = list(
      height = rnorm(5, 170) |> as.integer(),
      weight = rnorm(5, 80) |> as.integer(),
      sex = sample(c("M", "F", NA), 5, TRUE)
    )
  )
)

Turning this list inside out means manipulating this list such that height, weight and sex become the surface-level elements and the groups become the deepest levels.

This can be done fast & easy with ‘broadcast’, by casting the nested list to dimensional with in2out = TRUE, and then casting the dimensional list back to nested using in2out = FALSE, like so:

x2 <- cast_hier2dim(x)
dimnames(x2) <- hiernames2dimnames(x)
x3 <- cast_dim2hier(x2, in2out = FALSE, distr.names = TRUE)
lobstr::tree(x3)
#> <list>
#> ├─height: <list>
#> │ ├─class1: <list>
#> │ │ ├─group1<int [5]>: 170, 171, 168, 171, 168
#> │ │ └─group2<int [5]>: 169, 171, 169, 169, 171
#> │ └─class2: <list>
#> │   ├─group1<int [5]>: 170, 169, 170, 170, 169
#> │   └─group2<int [5]>: 170, 169, 169, 168, 169
#> ├─weight: <list>
#> │ ├─class1: <list>
#> │ │ ├─group1<int [5]>: 80, 81, 79, 79, 80
#> │ │ └─group2<int [5]>: 81, 79, 78, 79, 80
#> │ └─class2: <list>
#> │   ├─group1<int [5]>: 80, 79, 79, 82, 77
#> │   └─group2<int [5]>: 80, 79, 81, 79, 80
#> └─sex: <list>
#>   ├─class1: <list>
#>   │ ├─group1<chr [5]>: "F", "NA", "M", "M", "NA"
#>   │ └─group2<chr [5]>: "F", "F", "F", "F", "F"
#>   └─class2: <list>
#>     ├─group1<chr [5]>: "M", "M", "NA", "NA", "M"
#>     └─group2<chr [5]>: "F", "F", "NA", "NA", "F"

Easy, right?